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The local sapient species on a relatively Earthlike planet has constructed a space elevator. It is anchored along the equator. Due to unfortunate circumstances (and potentially divine intervention) the elevator's counterweight (presumably still connected somehow to the tether) falls back towards the planet, striking an ice cap at the north pole.

More specifically, I'd like to know how hard it would hit the planet. Information on what the fallout of such an impact would be (ie if it'd kick up tsunamis or shockwaves of any kind) would be nice, but is not necessary. I understand that a space elevator's counterweight falling back to the planet is unlikely in reality; I'm interested specifically in the impact itself, not necessarily the events that set it into motion.

You can fudge some of the numbers and details about the exact size/composition of the elevator as necessary. I'm presuming that the anchor is situated directly on the equator of a planet with Earth's mass, with the counterweight at about 62,000 miles above the planet's surface. The counterweight and tether are constructed out of a biomechanical latticework of organic material and inorganic cables, strong enough to withstand the stresses placed upon them. The counterweight itself is a partially-hollow spacedock meant for launching spacecraft beyond the planet. I sadly can't find any sources on what the mass of a space elevator's counterweight is expected to be, but the presume that the planet it's orbiting is more or less the same as Earth (same mass, same rotational speed, same composition, etc.)

EDIT: Updated with more details on the elevator.

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  • $\begingroup$ How sapient are the species who built space elevator at the North Pole and expected it to stay afloat? $\endgroup$ – Alexander Apr 30 '20 at 0:20
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    $\begingroup$ @Alexander The elevator isn't tethered at the north pole, the counterweight simply fell to the north pole. $\endgroup$ – MUSE-42 Apr 30 '20 at 0:21
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    $\begingroup$ When you break a Space Elevator, the counterweight doesn't fall onto the planet. The counterweight winds up in an elliptical orbit with the periapsis at where the counterweight was when the break happens. You have to work hard to make the counterweight hit the planet. It's less work to run it up to escape velocity. $\endgroup$ – notovny Apr 30 '20 at 0:58
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    $\begingroup$ I've voted to reopen. You do need to pick a mass for the counterweight. The counterweight in an elevator is usually about the weight of the car + 0.5 the max load. The rules are a bit different for a space elevator, but likely not an issue. So, pick your max weight, then let's say the car is 5% of that max, so 0.55 * max load. Edit your question with that and IMO there's enough to answer the question. $\endgroup$ – JBH Apr 30 '20 at 13:13
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    $\begingroup$ Agreement with JBH. The question cannot be answered unless there is a mass for the counterweight. Literally all the physics math for the impact rely on that number. I will vote reopen, but if you don't get a number in there soon it won't last long. $\endgroup$ – TitaniumTurtle Apr 30 '20 at 16:41
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Assumption: Earth conditions, should happen similarly on other planets too.

  1. Taken for granted: the counterweight lands on North Pole (unusual given that the g of the counterweigh is away from Earth, dominated by centrifugal force, to keep the cable in tension; the most likely scenario would have the counterweight projected into space). Given the counterweight was on an equatorial orbit, very likely the impact will be very close to tangential (grazing incidence - 5degrees or so). Which means a longer transit through atmosphere, the impact will project the majority of the ejecta in space. A non-trivial proportion will fall back onto Earth, a number of secondary Tunguska-event-like in magnitude will happen, but the majority of impact energy will be carried away by the ejecta. An example of oblique impact on the Moon is the Messier crater

  2. the second thing to remember is the cable itself. Unless someone handwaves an unobtainium tensile material (thus thin), the cable is gonna have a considerable thickness (even when tapered) and mass. Even more, the length of the cable will be 2.5-3 x the diameter of the planet, as it needs to reach well beyond the geostationary orbit. Which means if the entire cable falls back on Earth, it will circle the Earth for some length (and time) - expect hypersonic velocities towards the end of the cable fall; a whip of thousands of tones going across the skies, burning through the atmosphere and going some 3 times around around the world.

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A better question would be HOW this would happen. You honestly need to rework your entire situation.

I'd use the word plummet, not fall, because it wouldn't fall. However, some things might destablize it's orbit pattern causing it to uncontrollably change trajectory.

Most notably a very large passing object or collision could throw it into a heavy inclination (we are talking something the size of a medium sized moon) and the north-south stabilization tethers could sheer off. With enough force this could cause the elevator to destablize enough to enter the upper atmosphere where it would break off the remaining tethers and go into an aerobreak decaying orbit.

This would then take a few weeks to a few months before the orbit would completely decay resulting in a collision anywhere on the planet.

This is not something that would happen overnight, and a lot of the velocity would be absorbed in the atmosphere, and like any object entering the atmosphere at orbital velocity, most of the counterweight would burn off. The impact would simply occur at a high terminal velocity similar to a large meteor.

For the sake of making the situation work presume the counterweight is well shielded and very large. Otherwise it would simply burn up.

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  • $\begingroup$ Ah, fascinating! The planet does have a rather large moon, although I'd bet that the elevator was constructed with its gravitational disturbances in mind. I'll keep this in mind as I develop the idea! $\endgroup$ – MUSE-42 Apr 30 '20 at 2:59
  • $\begingroup$ I'm not sure I understand the scenario you are describing. Are you saying that the tether would get dragged through the atmosphere and that pull on the counter weight enough to bring it down? $\endgroup$ – Harabeck May 1 '20 at 20:16

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